Bootstrapping One-Loop QCD Amplitudes with General Helicities
Abstract
The recently developed on-shell bootstrap for computing one-loop amplitudes in non-supersymmetric theories such as QCD combines the unitarity method with loop-level on-shell recursion. For generic helicity configurations, the recursion relations may involve undetermined contributions from non-standard complex singularities or from large values of the shift parameter. Here we develop a strategy for sidestepping difficulties through use of pairs of recursion relations. To illustrate the strategy, we present sets of recursion relations needed for obtaining n-gluon amplitudes in QCD. We give a recursive solution for the one-loop n-gluon QCD amplitudes with three or four color-adjacent gluons of negative helicity and the remaining ones of positive helicity. We provide an explicit analytic formula for the QCD amplitude A6;1(1-,2-,3-,4+,5+,6+), as well as numerical results for A7;1(1-,2-,3-,4+,5+,6+,7+), A8;1(1-,2-,3-,4+,5+,6+,7+,8+), and A8;1(1-,2-,3-,4-,5+,6+,7+,8+). We expect the on-shell bootstrap approach to have widespread applications to phenomenological studies at colliders.
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